The businessman revealed in an exclusive interview with The Evening Times yesterday that he could plough up to £50million into the Light Blues to ensure they are in shape on and off the field ahead of their expected return to the SPFL Premiership the season after next.
The League One champions are due to release their interim financial accounts in the coming weeks, but King is eager to lead a fresh round of fund-raising at Ibrox.
A statement from the Rangers Union of Fans said: "It was clear from our discussions with him last week that the £30m+ Mr King is willing to invest is crucial to take the club back to a competitive level and improve the infrastructure and facilities. The club has been neglected - that cannot continue.
"Only once this investment has been made will Rangers be able to live within its means, something we all want for the longer term future.
"We would now ask the board to indicate publicly, as a matter of urgency, whether they are prepared to accept Dave King's offer of massive investment. The ball is firmly with the Rangers PLC board, in particular with chief executive officer Graham Wallace and chairman David Somers.
"Dave King has put a figure on what Rangers need and has shown his commitment to, and ambition for, the club he has supported all his life. Do Mr Wallace and Mr Somers agree with his figures and if they do, how do they propose to raise this large sum of money without Dave King?"
Meanwhile, Rangers have confirmed that the controversial loan given to the club by shareholders Laxey Partners Ltd has been transferred to lifelong supporter George Letham.
Laxey and Greenock businessman Sandy Easdale loaned a combined £1.5million to the Gers last month but Mr Letham has now taken up the Hedgefund's £1million portion that will see him recoup just £45,000 in interest rather than the £150,000 agreed in the original deal.